the car needs washed
Is there a name/term for this abomination? I’ve only ever heard one person speak in that form (omitting “to be”), and it has haunted me ever since.
I think you’d call this elision. Assume that the phrase is originally “the car needs to be washed” but you cut out “to be”, making it into a shorter form. It’s pretty common in language to shorten things to make it faster to speak. Think of the endless contractions in English or perhaps leaving part of a sentence completely unspoken because the content is easily assumed by the interlocutors.
Worse, to me, is that there is a perfectly grammatically correct way to be just as brief.
Wrong:
The bed sheets need washed.
Right:
The bed sheets need washing.